A pie chart has three sectors representing the distribution of budget into education (45°), healthcare (90°), and infrastructure (225°). What is the percentage of the budget alloca... A pie chart has three sectors representing the distribution of budget into education (45°), healthcare (90°), and infrastructure (225°). What is the percentage of the budget allocated to healthcare? In a stacked bar diagram, a company’s quarterly profits are divided into domestic and international categories. If Q1 shows 60% domestic and 40% international, and Q1 total profit is $200,000, what is the value of the international profit for Q1?
Understand the Problem
The question is asking to calculate percentages related to budget allocation in a pie chart and to determine the value of international profit given a total profit amount and profit distribution percentages.
Answer
Healthcare budget percentage: $25\%$, International profit for Q1: $80,000$.
Answer for screen readers
The percentage of the budget allocated to healthcare is $25%$, and the value of international profit for Q1 is $80,000$.
Steps to Solve
- Calculate Percentage of Budget Allocated to Healthcare
First, we need to find the total angle of the pie chart. The total angle in a pie chart is $360^\circ$.
The angle for healthcare is $90^\circ$.
To find the percentage allocated to healthcare, use the formula:
$$ \text{Percentage} = \left( \frac{\text{Healthcare Angle}}{\text{Total Angle}} \right) \times 100 $$
Plugging in the values:
$$ \text{Percentage} = \left( \frac{90}{360} \right) \times 100 = 25% $$
- Calculate International Profit for Q1
In this step, we identify the proportions of domestic and international profits. We know the total profit is $200,000$, and the international profit represents $40%$ of the total profit.
To calculate the international profit, we use:
$$ \text{International Profit} = \text{Total Profit} \times \left( \frac{\text{International Percentage}}{100} \right) $$
Substituting the known values:
$$ \text{International Profit} = 200,000 \times \left( \frac{40}{100} \right) = 200,000 \times 0.4 = 80,000 $$
The percentage of the budget allocated to healthcare is $25%$, and the value of international profit for Q1 is $80,000$.
More Information
In a pie chart, each sector represents a part of a whole, and the total angle helps determine the percentage for any given sector. Similarly, profit distribution can be easily calculated using simple percentage formulas.
Tips
- For the pie chart: A common mistake is forgetting to compare the healthcare angle to the total angle of $360^\circ$.
- For the profit calculation: Students might forget to convert the percentage into a decimal before multiplying it with the total profit.
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